Following is the data showing battery lives in hours for four different brands of smartphones published in an article ba

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Following is the data showing battery lives in hours for four
different brands of smartphones published in an article based on
reviews comparisons of products in a laboratory:
(a) State the assumptions for testing equality of mean battery
lives 𝜇𝐴, 𝜇𝐵, 𝜇𝐶, 𝜇𝐷 for the given four brands.
(b) Write down the formula for the point estimate of the
variance 𝜎 2 for the battery life of a smartphone and calculate it
for the given problems.
(c) Write down the formulae, probability distributions and
degrees of freedom for the sum of squares in this test once you
divide them by the variance 𝜎 2 ?
(d) How do you calculate the F ratio that is used as the
computed value of the test statistic for the appropriate test
needed here?
(e) Mention the point estimate its probability distribution for
the contrast 𝜇𝐴 + 𝜇𝐵 + 𝜇𝐶 − 3𝜇𝐷. What will be the computed test
statistic for testing the null hypothesis for this contrast,
namely, 𝐻0: 𝜇𝐴 + 𝜇𝐵 + 𝜇𝐶 − 3𝜇𝐷 = 0?
(f) Construct a single ANOVA table showing F ratios for both (d)
and (e).
(g) At 1% level of level of significance, what are your
conclusions for the above two F tests using the p-value
approach.
(h) Use Tukey’s test to determine which smartphones are
different from each other in terms of mean battery lives.
(i) Use Duncan’s test to determine which smartphones are
different from each other in terms of mean battery lives.
(j) Use Bartlett’s test to check if the homoscedasticity
assumption is valid in this problem.